https://doi.org/10.1140/epjs/s11734-026-02452-2
Regular Article
Mobility in spatial biodiversity models through recurrence quantification analysis
1
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Telegrafenberg A31, 14473, Potsdam, Germany
2
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13560-970, São Carlos, SP, Brazil
3
Departamento de Física, Universidade Federal da Paraíba, 58051-970, João Pessoa, PB, Brazil
a
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Received:
31
January
2026
Accepted:
4
June
2026
Published online:
2
July
2026
Abstract
Recurrence plots (RPs) and their associated quantifiers provide a robust framework for detecting and characterizing complex patterns in non-linear time-series. We employ recurrence quantification analysis (RQA) to investigate the dynamics of the cyclic, non-hierarchical May–Leonard model (rock–paper–scissors), which captures competitive interactions among three species. A crucial control parameter is the species’ mobility m, which governs spatial displacement and strongly shapes the dynamics. By systematically varying m and constructing RPs from numerical simulations, we examine how recurrence quantifiers reflect distinct dynamical features associated with different ecological states. We then introduce an ensemble-based approach that leverages statistical distributions of quantifiers across many independent realizations to identify dynamical outliers, defined as significant deviations from typical system behaviour. Detailed numerical analyses show that these outliers correspond to divergent ecological regimes at specific mobility values and provide a robust route to infer m from observed data. Overall, our results highlight recurrence-based methods as effective diagnostics for spatial ecological systems, enabling the extraction of ecologically relevant information from non-linear dynamical patterns.
© The Author(s) 2026
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